(English native speaker here) What do you want for a present? is best. The other one is wrong. If I was asking someone this in real life, I would say: What would you like as a present? "what do you want" is a bit too direct in English

Both sentences are correct, but they have slightly different wordings: "What do you want for a present?" "What do you want for present?" The first sentence is more commonly used and sounds more natural in English. However, both convey the same meaning, and the choice between them might depend on personal preference or regional language variations.

The first isn’t wrong, but not too efficient. Alternatives: What present do you want? What present would you like? What do you want for your birthday? (Present is understood) And in your sentence you can use ‘as’ to replace ‘for’ with a similar feel

a present